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#!/usr/bin/env python
#
# Copyright 2004 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# GNU Radio is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3, or (at your option)
# any later version.
#
# GNU Radio is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with GNU Radio; see the file COPYING. If not, write to
# the Free Software Foundation, Inc., 51 Franklin Street,
# Boston, MA 02110-1301, USA.
#
import re
import math
import sys
import operator
import numpy
from gnuradio import trellis
try:
import scipy.linalg
except ImportError:
print "Error: Program requires scipy (see: www.scipy.org)."
sys.exit(1)
######################################################################
# Decimal to any base conversion.
# Convert 'num' to a list of 'l' numbers representing 'num'
# to base 'base' (most significant symbol first).
######################################################################
def dec2base(num,base,l):
s=range(l)
n=num
for i in range(l):
s[l-i-1]=n%base
n=int(n/base)
if n!=0:
print 'Number ', num, ' requires more than ', l, 'digits.'
return s
######################################################################
# Conversion from any base to decimal.
# Convert a list 's' of symbols to a decimal number
# (most significant symbol first)
######################################################################
def base2dec(s,base):
num=0
for i in range(len(s)):
num=num*base+s[i]
return num
######################################################################
# Automatically generate the lookup table that maps the FSM outputs
# to channel inputs corresponding to a channel 'channel' and a modulation
# 'mod'. Optional normalization of channel to unit energy.
# This table is used by the 'metrics' block to translate
# channel outputs to metrics for use with the Viterbi algorithm.
# Limitations: currently supports only one-dimensional modulations.
######################################################################
def make_isi_lookup(mod,channel,normalize):
dim=mod[0]
constellation = mod[1]
if normalize:
p = 0
for i in range(len(channel)):
p = p + channel[i]**2
for i in range(len(channel)):
channel[i] = channel[i]/math.sqrt(p)
lookup=range(len(constellation)**len(channel))
for o in range(len(constellation)**len(channel)):
ss=dec2base(o,len(constellation),len(channel))
ll=0
for i in range(len(channel)):
ll=ll+constellation[ss[i]]*channel[i]
lookup[o]=ll
return (1,lookup)
######################################################################
# Automatically generate the signals appropriate for CPM
# decomposition.
# This decomposition is based on the paper by B. Rimoldi
# "A decomposition approach to CPM", IEEE Trans. Info Theory, March 1988
# See also my own notes at http://www.eecs.umich.edu/~anastas/docs/cpm.pdf
######################################################################
def make_cpm_signals(K,P,M,L,q,frac):
Q=numpy.size(q)/L
h=(1.0*K)/P
f0=-h*(M-1)/2
dt=0.0; # maybe start at t=0.5
t=(dt+numpy.arange(0,Q))/Q
qq=numpy.zeros(Q)
for m in range(L):
qq=qq + q[m*Q:m*Q+Q]
w=math.pi*h*(M-1)*t-2*math.pi*h*(M-1)*qq+math.pi*h*(L-1)*(M-1)
X=(M**L)*P
PSI=numpy.empty((X,Q))
for x in range(X):
xv=dec2base(x/P,M,L)
xv=numpy.append(xv, x%P)
qq1=numpy.zeros(Q)
for m in range(L):
qq1=qq1+xv[m]*q[m*Q:m*Q+Q]
psi=2*math.pi*h*xv[-1]+4*math.pi*h*qq1+w
#print psi
PSI[x]=psi
PSI = numpy.transpose(PSI)
SS=numpy.exp(1j*PSI) # contains all signals as columns
#print SS
# Now we need to orthogonalize the signals
F = scipy.linalg.orth(SS) # find an orthonormal basis for SS
#print numpy.dot(numpy.transpose(F.conjugate()),F) # check for orthonormality
S = numpy.dot(numpy.transpose(F.conjugate()),SS)
#print F
#print S
# We only want to keep those dimensions that contain most
# of the energy of the overall constellation (eg, frac=0.9 ==> 90%)
# evaluate mean energy in each dimension
E=numpy.sum(numpy.absolute(S)**2,axis=1)/Q
E=E/numpy.sum(E)
#print E
Es = -numpy.sort(-E)
Esi = numpy.argsort(-E)
#print Es
#print Esi
Ecum=numpy.cumsum(Es)
#print Ecum
v0=numpy.searchsorted(Ecum,frac)
N = v0+1
#print v0
#print Esi[0:v0+1]
Ff=numpy.transpose(numpy.transpose(F)[Esi[0:v0+1]])
#print Ff
Sf = S[Esi[0:v0+1]]
#print Sf
return (f0,SS,S,F,Sf,Ff,N)
#return f0
######################################################################
# A list of common modulations.
# Format: (dimensionality,constellation)
######################################################################
pam2 = (1,[-1, 1])
pam4 = (1,[-3, -1, 3, 1]) # includes Gray mapping
pam8 = (1,[-7, -5, -3, -1, 1, 3, 5, 7])
psk4=(2,[1, 0, \
0, 1, \
0, -1,\
-1, 0]) # includes Gray mapping
psk8=(2,[math.cos(2*math.pi*0/8), math.sin(2*math.pi*0/8), \
math.cos(2*math.pi*1/8), math.sin(2*math.pi*1/8), \
math.cos(2*math.pi*2/8), math.sin(2*math.pi*2/8), \
math.cos(2*math.pi*3/8), math.sin(2*math.pi*3/8), \
math.cos(2*math.pi*4/8), math.sin(2*math.pi*4/8), \
math.cos(2*math.pi*5/8), math.sin(2*math.pi*5/8), \
math.cos(2*math.pi*6/8), math.sin(2*math.pi*6/8), \
math.cos(2*math.pi*7/8), math.sin(2*math.pi*7/8)])
orth2 = (2,[1, 0, \
0, 1])
orth4=(4,[1, 0, 0, 0, \
0, 1, 0, 0, \
0, 0, 1, 0, \
0, 0, 0, 1])
######################################################################
# A list of channels to be tested
######################################################################
# C test channel (J. Proakis, Digital Communications, McGraw-Hill Inc., 2001)
c_channel = [0.227, 0.460, 0.688, 0.460, 0.227]
if __name__ == '__main__':
f1=trellis.fsm('fsm_files/awgn1o2_4.fsm')
#f2=trellis.fsm('fsm_files/awgn2o3_4.fsm')
#print f1.I(), f1.S(), f1.O()
#print f1.NS()
#print f1.OS()
#print f2.I(), f2.S(), f2.O()
#print f2.NS()
#print f2.OS()
##f1.write_trellis_svg('f1.svg',4)
#f2.write_trellis_svg('f2.svg',4)
#f=fsm_concatenate(f1,f2)
#f=fsm_radix(f1,2)
#print "----------\n"
#print f.I(), f.S(), f.O()
#print f.NS()
#print f.OS()
#f.write_trellis_svg('f.svg',4)
q=numpy.arange(0,8)/(2.0*8)
(f0,SS,S,F,Sf,Ff,N) = make_cpm_signals(1,2,2,1,q,0.99)
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